1. Let's start by stating the problem: We want to find the upper and lower bounds of a number, whether it is a whole number or a decimal. 2. The upper bound of a number is the smallest number that is greater than or equal to the given number but less than the next possible number in the context (like the next whole number or decimal place). 3. The lower bound is the largest number that is less than or equal to the given number but greater than the previous possible number. 4. For whole numbers, if the number is $n$, the lower bound is $n - 0.5$ and the upper bound is $n + 0.5$ because whole numbers are spaced by 1. 5. For decimal numbers, the bounds depend on the place value of the last digit. For example, if the number is rounded to the nearest tenth, the lower bound is the number minus half of $0.1$ (which is $0.05$), and the upper bound is the number plus $0.05$. 6. In general, if the number is rounded to the nearest $d$, the bounds are: $$\text{Lower bound} = \text{number} - \frac{d}{2}$$ $$\text{Upper bound} = \text{number} + \frac{d}{2}$$ 7. Example: For the number 7 rounded to the nearest whole number, the bounds are: $$7 - 0.5 = 6.5$$ $$7 + 0.5 = 7.5$$ 8. Example: For the number 3.4 rounded to the nearest tenth, the bounds are: $$3.4 - 0.05 = 3.35$$ $$3.4 + 0.05 = 3.45$$ This method helps us understand the range within which the actual number lies based on its rounding.